Answer:
9, 23, 45, 75, 113, 159
Explanation:
Quadratic Sequence
The difference between two consecutive terms of a quadratic sequence is another sequence, this one is an arithmetic sequence.
The first terms are given as:
9, 23, 45, 75, ...
Let's compute the differences:
23 - 9 = 14
45 - 23 = 22
75 - 45 = 30
Note the differences form an aritmetic sequence of commons difference 8.
The next two terms will be formed adding 8 to the previous difference, that is:
30 + 8 = 38 is the next difference. And the next term is
75 + 38 = 113
38 + 8 = 46 is the next difference, and the next term is
113 + 46 = 159
Thus, the complete sequence is
9, 23, 45, 75, 113, 159